diff --git a/array_api_strict/_data_type_functions.py b/array_api_strict/_data_type_functions.py
index 046dfc7..acd8967 100644
--- a/array_api_strict/_data_type_functions.py
+++ b/array_api_strict/_data_type_functions.py
@@ -42,6 +42,13 @@ def astype(
 
     if not copy and dtype == x.dtype:
         return x
+
+    if isdtype(x.dtype, 'complex floating') and not isdtype(dtype, 'complex floating'):
+        raise TypeError(
+            f'The Array API standard stipulates that casting {x.dtype} to {dtype} should not be permitted. '
+             'array-api-strict thus prohibits this conversion.'
+        )
+
     return Array._new(x._array.astype(dtype=dtype._np_dtype, copy=copy), device=device)